4 Background P&C coverages Contracts are normally one year in duration - A few exceptions e.g., Japanese claim free savings contracts - Range from short-tail property to long-tail liability - Can include right of termination by one or both parties during the period Approaches described here also applicable to self-insurance and reinsurance Page 4

5 Background Claims groupings Similar types of claims are grouped to enhance accuracy of estimation process - By coverage With similar payment patterns If loss ratio is used, similar profit and expense margins - By period of claim incurral - But experience should be large enough to be reliable A single contract can contain several coverages - Automobile damage to vehicle, liability, collision, medical payments, uninsured motorists, - Commercial packages property and liability Page 5

8 Background Loss year Types of claims groupings - Accident / loss / report year - Calendar period of loss - Underwriting / policy year - Contracts written in period - Overlaps two calendar years - Used by Lloyd s In some cases, quarterly or semi-annual periods Subsequently measured by period since loss date Page 8

11 Basic approach Actuarially sound reserves Based on estimates Derived from reasonable assumptions Using appropriate methods Inherent uncertainty In part due to time to settle Conceptually a range of values True value known only after all claims settled Page 11

12 Basic approach (continued) Estimates - Of ultimate losses by period of claims, their components, their timing, associated premiums (if loss ratios used) and their probability distribution (if stochastic methods used) - Data used almost always entity-specific where relevant - May be supplemented by industry experience when company doesn t have sufficient relevant experience - Limited relevant market experience - Based on financial reporting context, e.g., level of prudence Same approaches used for direct insurance, reinsurance and self-insurance Page 12

15 The loss development triangle What is it? Follows a cohort of similar claims incurred within a period through each subsequent reporting period to measure loss component patterns and trends to estimate patterns of future activity Can be used with - Cumulative paid losses - Incurred losses = cumulative paid losses + case reserves at end of each period - Number of claims - Size of claims - Case reserves Page 15

16 The loss development triangle (continued) Why is it used so often? - A useful way of both thinking about and presenting the emergence of claims information over time - Components usually exhibit identifiable trends over time - Makes estimating ultimate losses easier Number of years included in triangle varies by - Data available - Type of loss (e.g., speed of payment) - Relevancy of losses of older periods Diagonals represent status or activity at a measurement date or during specific calendar period Page 16

19 The loss development triangle (continued) Patterns shown are multiplicative, evidenced by - Current period value divided by that of prior period - Link or loss development factors Ratios of losses at successive evaluations for a defined group of claims (e.g., accident year) The triangle is actually a rectangle - Experience in upper left triangle - Objective estimating bottom right triangle - Looks easy, but judgment always needed Page 19

22 Types of loss reserve methods (continued) 5. Bornhuetter-Ferguson - Weighted average (based on percentage expected to be reported) of Incurred (or paid) claims to date Initial (or updated) estimate of ultimate losses for claim cohort based on - Loss ratio or exposure x estimated loss per exposure - Used in most recent year or two or where limited reported losses to date such as assumed reinsurance 6. Many other methods Almost always multiple methods evaluated Page 22

23 Development method -- example Cumulative Paid (CU 000s) EZ INSURANCE COMPANY AUTO LIABILITY Accident Development State in Months Year Accident Paid Development Factors between months Year Ult Unweighted average point average Average excluding high/low Volume weighted average Selected LDFs Cumulative LDFs Page 23

24 Development method loss development factors Major assumption development is a multiplicative process Selected development factor for 2003, 12 to 24 month = 280 / 128 Cumulative development factor - Multiply all development factors from current point to last experience point times tail factor (to take to ultimate value) = 1.55 x x Applied to relevant diagonal value Warning not all triangles this well-behaved Page 24

26 The loss development triangle The tail Tail factor takes losses from experience in the triangle to their ultimate value - In example, takes losses after 7 years to their ultimate value - Difficult with limited data - Use industry or similar entity experience if relevant Results can be quite sensitive to tail - Because applied to cumulative losses - For example, a 2% change could result in a 40% increase in IBNR How Much Tail Can There Be? Development in Reinsured Layers Selected Cumulative Age to Ultimate Factors Source: Reinsurance Association of America data Line of Business 15 Years to Ultimate 25 Years to Ultimate Workers Compensation General Liability AL Treaty Page 26

29 Bornhuetter-Ferguson method Weighted average of results of development method and loss ratio method - Weight based on expected percentage reported at valuation time for a given accident period - Uses historical experience directly to estimate ultimate losses Several alternatives to loss ratio value can be used - Exposure x Exposure units (such as contracts inforce) - Expected claim frequency x expected average size claim - Prior estimate Used when insufficiently reliable reported claim experience to date or long-tail business, but don t want to ignore current results Page 29

30 Baseball example How many home runs will Barry Bonds hit this year, given: - He has hit 20 home runs through 40 games - There are 160 games in the season Information needed for estimate based on various actuarial methods - Expected Ultimate Value = 40 (before season started) - Factor to project Current Diagonal to Ultimate Value Current Diagonal = 20 home runs hit through ¼ of season Development method: 80 = 20 x 4 (4 = cumulative development factor) Loss ratio method: experience) 40 (initial expectation, unadjusted by Bornhuetter-Ferguson: 50 = 20 + ¾ x 40 (weighted average of experience and initial expectation, times percent of expected unreported) Choice depends on knowledge of his current health, whether he hits better in the spring or in the fall, Page 30

31 Some problems Choice or use of methods No method is perfect and no method can be applied in all situations In practice, common to use different methods for different periods since accident year, e.g. - Case reserves for oldest years - Development method for years Bornhuetter-Ferguson for most recent year Examine results from several methods for each time period Significant effect of changes in estimates on reserves and even greater effect on income Page 31

32 Some problems Uncertainty Significant uncertainty in estimates - Although a single number is needed for balance sheet - A range may be more appropriate, can be based on - Different methods, LDFs, probability distributions, - Judgment is always needed Must understand the business, claims process and environment If something can go wrong, it will Common to continue to refine data, assumptions and methods Page 32

33 Some problems Uncertainty and stochastic methods With increasing emphasis on effect of risk, stochastic methods have become more common Requires estimates of probability distribution of claim liability components - Ultimate loss, frequency, severity and timing Results in estimates of frequency distribution of possible outcomes - Can produce confidence intervals, with enhanced understanding of risks But danger of overstating the precision of the resulting estimate based on a further set of assumptions Page 33

36 Key Assumptions Potential Problems No inflation or if there has been, fully reflected in experience to date Inflation general or social/legal, that varies by calendar period or unequally by coverage types No data anomalies Catastrophic or unusual losses reflected in loss experience Unusual claim settlement/reporting delays Unusually large claim(s) If reinsurer, reporting problems with direct writers or lack of sufficient data Page 36

37 Monitoring results Retrospective testing Important to continue asking how assumptions performed - Through continual challenge of your own assumptions Applicable to each claim liability component Examples of questions to answer - How many new claims were expected this year - What average claim size was expected - Why was there a deviation from estimates Due to random fluctuation or changes in conditions that need to be reflected next time? Page 37

38 Disclosure The best way to monitor loss development for most lines is through loss triangles - Power and importance of how did we estimate - Retrospective loss triangles can show changes in loss reserve estimates over time - Meaningful period typically five or ten years, depending on the speed of claims closure, but earlier period may no longer be relevant Although discounted reserves can be used in a triangle, care is needed to compare diagonals on an apples-to-apples basis Page 38

Sec Description Pages 1 Introduction 84 2 Key Assumptions 84 3 Common Uses of the Development Technique 84-85 4 Mechanics of the Development Technique 85-92 5 Unpaid Claim Estimate Based on the Development

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